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A series of notes whose fundamental frequencies have definite ratios and which produce a pleasing effect on the ear when sounded in succession constitute a musical scale.

If the particles of a medium vibrate along the direction of wave propagation then wave is called longitudinal waves, e.g: Sound waves in air are longitudinal waves.

f_A = 341 H_z 

f = ? 

and f_b = 6 beats/s 

f_b= f_A ~ f_x 

or f = f_A ± f_b = 341 ± 6 

= 335 Hz or 347 Hz.

1. Doppler effect is used in a radar system to detect the speed of automobiles and aeroplanes. 

2. It is used to determine the speed submarines (Using SONAR). 

3. It is used to determine the speed of stars and planets and other celestial bodies.

1. When the prongs of a tuning fork are filed its frequency increases. 

2. The frequency of a tuning fork decreases when the prongs are waxed.

The apparent change in the frequency of sound due to the relative motion between the source and the observer is called the Doppler effect. 

E.g: The apparent frequency of the whistle of a train increases as it. approaches an observer on the platform and decreases when the train passes the observer.

The periodic rise and fall (Waxing and waning) in the intensity of sound due to the superposition of two sound waves of slightly different frequencies traveling in the same direction is called beats. The phenomenon of beats can be used. 

1. To determine the unknown frequency of a tuning fork. 

2. In tuning musical instruments.

(c) increase in frequency of sound only

Wave motion is a kind of disturbances which travels through a medium due to repeated vibrations of the particles of the medium about their mean positions, the disturbance being handed over form one particle to the next.

It is defined as the time which sound takes to fall in intensity to one million^th (10^-6) part of its original intensity after it was stopped.

If during the propagation of a wave through a medium the particles of the medium vibrate simple harmonically about their mean positions, than the wave is said to be plane progressive harmonic wave.

The phase of a harmonic is quantity that gives complete information of the wave at any time and at any position.

The persistence of audible sound after the source has ceased to emit sound is called reverberation.

The distance covered by a wave in the direction of its propagation per unit time is called the wave velocity.

The lowest intensity of sound that can be perceived by the human ear is called threshold of hearing. For a sound of frequency 10 kHz, the threshold of hearing is 10^-12 Wm^-2

Echo: An echo is a repetition of sound produced by the reflection of sound waves from a wall, mountain or other obstructing surfaces.

Explanation: The speed of sound in air at 20°C is 344 m s^-1 . If we shout at a wall which is at 344 m away, then the sound will take 1 second to reach the wall. After reflection, the sound will take one more second to reach us. Therefore, we hear the echo after two seconds. Scientists have estimated that we can hear two sounds properly if the time gap or time interval between each sound is \((\frac{1}{10})^{th}\) of a second (persistence of hearing) i.e., 0.1 s. Then,

Velocity = \(\frac{distance \,travelled}{Time\, taken}\) = \(\frac{2d}{t}\)

2d= 344 × 0.1 = 34.4m ;d= 17.2m 

The minimum distance from a sound reflecting wall to hear an echo at 20°C is 17.2 meter.

Suppose we drop a stone in a trough of still water, we can see a disturbance produced at the place where the stone strikes the water surface. We find that this disturbance spreads out (diverges out) in the form of concentric circles of ever increasing radii (ripples) and strike the boundary of the trough. This is because some of the kinetic energy of the stone is transmitted to the water molecules on the surface. Actually the particles of the water (medium) themselves do not move outward with the disturbance. This can be observed by keeping a paper strip on the water surface. The strip moves up and down when the disturbance (wave) passes on the water surface. This shows that the water molecules only undergo vibratory motion about their – mean positions.

When two identical waves of same amplitude and frequency travelling in opposite directionals with the same speed along the same path superpose each other, the resultant wave does not travel in the either direction and is called stationary or standing waves.

(c) increases with increase in humidity.

(c) wavelength of sound waves.

Wire of twice the length vibrates in its second harmonic. Thus if the tuning fork resonaters at L, it will resonate at 2L.

Interference is a phenomenon in which two waves superimpose to form a resultant wave of greater, lower or the same amplitude.

(b) 0.5 second

When two or more waves superimpose each other with slightly different frequencies, then a sound of periodically varying amplitude at a point is observed. This phenomenon is known as beats. The number of amplitude maxima per second is called beat frequency. If we have two. sources, then their difference in frequency gives the beat frequency. 

Number of beats per second n = | f₁ – f₂ | per second

(d) y=-0.4sin2π(t-c/2)

(d) there is no transfer of heat

The number of beats heard per second is called beat frequency.

The rise and fall in the intensity of sound due to the superposition of two sound waves of slightly different frequencies traveling in the same direction is known as beats.

The velocity of sound in a gas is directly proportional to the square root of the absolute temperature.

330 ms^-1 

[Reason: Velocity of sound in a gas is independent of pressure].

(b) density and elasticity of gas

(d) Always zero

The phase difference between two nearest crests is Zero or 2π

The relation between wavelength, wave velocity and frequency is v = νλ

We know that, the basic condition for an echo to be heard is that the obstacle should be rigid and of large size. Also the obstacle should be at least at a distance of 17m from the source. Since the length of the room is generally less than 17m, the conditions for the production of Echo are not satisfied. Hence no echo is heard in a room.